arXiv research

The paper improves the probability flow ODE sampler for faster sampling of natural images.

Revisits VIC method to correct intrinsic reward bias in stochastic environments.

Market activity scales near a constant of 0.632 in intrinsic time.

We present four models for a random graph and show that, in each case, the probability that a graph is intrinsically knotted goes to one as the number of vertices increases. We also argue that, for $k \geq 18$, most graphs of order $k$ are intrinsically knotted and, for $k \geq 2n+9$, most of order $k$ are not $n$-apex…

The paper examines Wiener process for LID estimation methods.

The paper reinterprets Bayesian priors and posteriors using Riemannian manifolds.

Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.

In this article, we study the geodesic problem in a generalized metric space, in which the distance function satisfies a relaxed triangle inequality $d(x,y)\leq σ(d(x,z)+d(z,y))$ for some constant $σ\geq 1$, rather than the usual triangle inequality. Such a space is called a quasimetric space. We show that many well-kn…

We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a basis for understanding these phenomena. In a continuous time framewo…

Estimates scalar curvature of point clouds without embedding.

Starting with Gilmer et al. (2018), several works have demonstrated the inevitability of adversarial examples based on different assumptions about the underlying input probability space. It remains unclear, however, whether these results apply to natural image distributions. In this work, we assume the underlying data …

Improved manifold-adaptive dimension estimator for better data complexity assessment.

Each compact manifold M of finite dimension k is differentiable and supports an intrinsic probability measure. There then exists a measurable transformation of M to the k-dimensional "surface" of the (k+1)-dimensional ball.

EOI enhances individuality in multi-agent systems.

The intrinsic entropy model accurately estimates stock market volatility.

This paper introduces a new method to compare collections of distributions on manifolds and graphs.

Many practical environments contain catastrophic states that an optimal agent would visit infrequently or never. Even on toy problems, Deep Reinforcement Learning (DRL) agents tend to periodically revisit these states upon forgetting their existence under a new policy. We introduce intrinsic fear (IF), a learned reward…

The paper analyzes the intrinsic exploration terms in policy-gradient algorithms.

We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied problem the Riemannian manifold $(M,g)$ is considered as an abstract metric space w…

Sharp bounds for high-probability estimation of discrete distributions.

If M is a smooth compact connected Riemannian manifold, let P(M) denote the Wasserstein space of probability measures on M. We describe a geometric construction of parallel transport of some tangent cones along geodesics in P(M). We show that when everything is smooth, the geometric parallel transport agrees with earli…

The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.

Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.

Shallow nonlinear networks can separate classes linearly with polynomially scaling width.

Deep networks can approximate high-dimensional distributions from low-dimensional ones.

A novel approach to computing barycenters on graph-supported probability measures.

We derive high-probability finite-sample uniform rates of consistency for $k$-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that $k$-NN regression adapts to an unknown lower intrinsic dimension automatically. We then apply the $k$-NN regression rates to establish new …

We characterise the link of derivatives in measure, which are introduced in [AKR,Card,ORS] respectively by different means, for functions on the space $\mathbb M$ of finite measures over a Riemannian manifold $M$. For a reasonable class of functions $f$, the extrinsic derivative $D^Ef$ coincides with the linear functio…

Unified high-probability regret bounds for online convex optimisation with randomised gradient estimators.

This study analyzes how well GANs approximate distributions from small samples.

Solves Monge-Ampère equations on compact Hessian manifolds using the Perron method.

Proposes tests for comparing high-dimensional manifold samples.

Paper improves deep learning convergence rates for low-dimensional data.

Unified framework for singular statistical models using observable charts.

In this paper, we develop and explore deep anomaly detection techniques based on the capsule network (CapsNet) for image data. Being able to encoding intrinsic spatial relationship between parts and a whole, CapsNet has been applied as both a classifier and deep autoencoder. This inspires us to design a prediction-prob…

Neural networks provide a rich class of high-dimensional, non-convex optimization problems. Despite their non-convexity, gradient-descent methods often successfully optimize these models. This has motivated a recent spur in research attempting to characterize properties of their loss surface that may explain such succe…

Geometrically, high-likelihood regions in DGMs are unlikely to generate OOD data.

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

A new method estimates Schrödinger bridges without iterative simulations or neural networks.

The article introduces inferential moments for analyzing uncertain multivariable systems.

We propose a method to assess the intrinsic risk carried by a financial position $X$ when the agent faces uncertainty about the pricing rule assigning its present value. Our approach is inspired by a new interpretation of the quasiconvex duality in a Knightian setting, where a family of probability measures replaces th…

GANs learn distributions well from samples, with rates depending on intrinsic dimension.

The paper studies the geometry of probability measures on the unit circle.

Model predicts default risk based on company's financial forecasts and credit conditions.

It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method…

With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification u…

DADApy analyzes high-dimensional data manifolds in Python.

Survey of intrinsically linked or knotted graphs.